How far can a human eye see? What is its power?

Michel van Biezen makes great educational videos and you can learn a lot of things from there. One of his videos teaches us how to calculate the power of the eye.

It turns out that the human eye, with an aperture of 4mm in the iris, can distinguish two objects that are 3 meters apart from a 20 km distance. Of course, you need perfect vision, weather and the object need to have some contrast.

The formula used to calculate this is
sin θ = 1.22 λ / D
λ – is the wavelength of the light
θ – is the angle at which you see the objects and is very, very small
D – is the diameter of the iris, 4 mm average

You can make
sin θ = tan θ = d / L
d – is the height of the object or the distance between two points
L – distance to object

This way you will be able to see an object that is 3 meters height or two objects that are 3 meters apart at 20 km. At 100 m you can see an object as small as 1.5 cm. Yup, the eye is pretty amazing.